The density of a solution containing 7.3% by mass of HCl is 1.2 g/mL. Calculate the molarity of the solution

Answer

To calculate the molarity of a solution containing 7.3% by mass of HCl with a density of 1.2 g/mL, we will follow these steps:

### Step 1: Calculate the mass of the solution
First, we need to determine the mass of 1 liter (1000 mL) of the solution using its density.

\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]
\[ \text{Mass of solution} = 1.2 \, \text{g/mL} \times 1000 \, \text{mL} = 1200 \, \text{g} \]

### Step 2: Calculate the mass of HCl in the solution
Since the solution is 7.3% by mass of HCl, we can calculate the mass of HCl in the 1200 g of solution.

\[ \text{Mass of HCl} = \text{Mass of solution} \times \left( \frac{\text{Percentage of HCl}}{100} \right) \]
\[ \text{Mass of HCl} = 1200 \, \text{g} \times \left( \frac{7.3}{100} \right) = 87.6 \, \text{g} \]

### Step 3: Calculate the number of moles of HCl
Next, we need to calculate the number of moles of HCl using its molar mass. The molar mass of HCl is approximately 36.46 g/mol.

\[ \text{Number of moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molar mass of HCl}} \]
\[ \text{Number of moles of HCl} = \frac{87.6 \, \text{g}}{36.46 \, \text{g/mol}} \approx 2.40 \, \text{mol} \]

### Step 4: Calculate the molarity of the solution
Finally, we can calculate the molarity (M) of the solution using the formula:

\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
Since we have 1 liter of solution:

\[ \text{Molarity (M)} = \frac{2.40 \, \text{mol}}{1 \, \text{L}} = 2.40 \, \text{M} \]

### Final Answer
The molarity of the solution is **2.40 M**.

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